A method of conceptual analysis in philosophy in which you analyze your intuitions to find truths. For example, to find out what is 'right', you would find a concept of 'right' that you think sounds complete. 'Right is giving everyone as much freedom as possible' Then you (or others) can test it in as many theoretical situations as possible. Even one possible situation which your intuition doesn't like the way things work will call for a modification of the concept. 'Hitler would use this freedom to kill millions of people'. And so you modify it.
And this goes on until the concept is perfect.

Indeed, one way of characterising Analytic Philosophy would be as the philosophy taking the view that mathematical standards of truth and inference can and should be applied to natural language.

Analytic philosophers who are feeling particularly insecure about the validity of their discipline will tend to clutter up their papers with lots of logical notation, and quite often even their ordinary sentences will sound like they have been translated back into English from formulae in some exotic calculus.

At its best, it can expose outrageous and unsuspected incongruities and inconsistencies in one's assumptions, it can make the previously incomprehensible seem humdrum, or the humdrum inconceivable. At its worst it can be bombastic, sterile, vacuous and trite.

The term is most used to distinguish the modern Anglo-American trend from so-called Continental1 Philosophy, the tradition of European thinkers such as Kierkegaard, Nietzsche, Sartre, Heidegger and so on. Perhaps the leading contemporary critic of the Analytic school from the Continental tradition is the French philosopher Jacques Derrida who has lately adopted the term phallogocentrism to describe it.

Since, try as they might, academics cannot sever themselves utterly from the world, criticisms from 'outside' Analytic philosophy are now being given serious consideration by thinkers from within and around the Analytic tradition, some of whom would prefer to see themselves as post-Analytic. The most visible is Richard Rorty who has essayed a pragmatic critique.4

On the Analytic view, the way towards such a post-Analytic perspective is not clear. One would need a supervenient clarity, giving analysis its place in a wider schema. But the very word 'schema' might be thought to imply 'subject to analysis.'

1. One is reminded by the choice of this word of the legendary English newspaper headline: Fog in Channel: Continent Isolated.